Combinatorics Calculator
Calculate permutations and combinations. With and without repetition. Online calculator with solution path and worked examples.
Arrangements without repetition
Result
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Formula
P(n,k) = n! / (n-k)!
Note: These calculations are for informational purposes only and do not replace professional tax or financial advice. All information without guarantee.
Frequently Asked Questions
What is the difference between permutations and combinations?
Permutations count arrangements where order matters (ABC is different from BAC). Combinations count selections where order does not matter (ABC and BAC are the same).
How do I calculate the number of possible combinations?
Combinations: C(n,k) = n! / (k! times (n-k)!). For example, choosing 3 items from 10: C(10,3) = 120. The exclamation mark denotes factorial (e.g., 5! = 120).
What is the Combinatorics Calculator?
The combinatorics calculator computes permutations, combinations and variations with and without repetition.
How does the Combinatorics Calculator work?
Choose the calculation type: permutation (arrangement of all elements), combination (selection without order) or variation (selection with order). The calculator computes the count and shows the formula.
Key Data and Facts
Permutation: n! Combination without repetition: n! / (k! * (n-k)!). Variation without repetition: n! / (n-k)!. Factorial: n! = 1 * 2 * ... * n.
Step-by-Step Guide
How to use den Kombinatorik-Rechner step by step: 1. Berechnungsart choose -- Permutation (alle Elemente anordnen), Kombination (Auswahl ohne Reihenfolge) oder Variation (Auswahl mit Reihenfolge). 2. Parameter enter -- n = Gesamtanzahl der Elemente, k = Anzahl der auszuwaehlenden Elemente. 3. Wiederholung festlegen -- mit Wiederholung bedeutet, dass Elemente mehrfach gewaehlt werden duerfen. 4. Formeln verstehen: Permutation ohne Wiederholung = n!. Kombination ohne Wiederholung = n! / (k! * (n-k)!), auch als Binomialkoeffizient (n ueber k) bekannt. Variation ohne Wiederholung = n! / (n-k)!. 5. Praktische Anwendungen: Lotto-Wahrscheinlichkeiten calculate (6 aus 49 = 13.983.816 Kombinationen), Sitzordnungen planen, PIN-Codes zaehlen (4 Ziffern mit Wiederholung = 10.000 Moeglichkeiten). Tipp: Fakultaet waechst extrem schnell -- 10! = 3.628.800, 20! hat bereits 19 Stellen.
Calculation Example
Kombination 6 aus 49 (Lotto): 49! / (6! * 43!) = 13.983.816. Variation 3 aus 10 ohne Wiederholung: 10! / 7! = 720.
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